$P$ is the LCM of $2, 4, 6, 8, 10, Q$ is the LCM of $1, 3, 5, 7, 9$ and $L$ is the LCM of $P$ and $Q$ . Then, which of the following is true ?

L=21P

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L=4Q

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L=63P

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L=16Q

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Solution

The correct option is A ( $L = 21 P$ )
Given $P$ is the LCM of $2, 4, 6, 8, 10$
So, lets find LCM:

Thus, $P = 2 \times 2 \times 3 \times 2 \times 5$
$∴ P = 120$ ....(i)
$Q$ is the LCM of 1 $, 3, 5, 7, 9 :$
So,

$Q = 3 \times 5 \times 7 \times 3$
$∴ Q = 315$ ......(ii)
$L$ is the LCM of $P, Q$ :
So, from equations (i) and (ii)

$\Rightarrow L = 21 \times 3 \times 5 \times 8 = 21 (120)$
$∴ L = 21 (P)$

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